Upgrading from a previous version to JEM4 requires a procedure to follow. It's not as simple as 1,2,3, please read the following instructions carefully:

1) Preparations

Make a backup!
Update to Joomla! 3.10.12
Update to JEM 2.3.6 (Premigration version), if not already done.
Make a new backup!
If you have template overrides for JEM: save them. You will have to adapt them after the update. Then disable them in the template folder (renaming them e.g. from "mod_jem" to "mod_jem_backup" is sufficient)
Disable all JEM extensions, component, all JEM plugins, all JEM modules. DON'T uninstall!
(During upgrade process, it's suggested to switch to Joomla3 default template "Protostar")

2) Update to Joomla4

To prepare the update from Joomla3 to Joomla4, go to Components > Joomla! Updates, choose Options and in Update Channel choose:
Joomla Next

You'll get now the informations about which other components are not ready to migrate. Perhaps you have to disable/uninstall other components/modules/plugins not prepared for Joomla4)

Update to php 8+
Then upgrade from Joomla3 to Joomla4.

3) Installation of JEM 4

Install JEM 4 (via upload or web installer)
Before switching to the frontend, change the positions of the JEM-modules and the main menue module, to the positions of your new Joomla4 template (e.g. the Joomla4 default template "cassiopeia")

If you get a red window, go to configuration>site>SEO and disable URL rewrite (htaccess)

Enable all JEM 4 (component, modules, plugins)
Adapt the JEM settings (there are changes: e.g. datetime format)
Adapt the JEM template overrides of necessary and reactivate them

Check everything, if it works!
Finished :-)